Elliptic curve data - 54978.bo3

Formats: - HTML - YAML - JSON - 2024-04-27T17:13:26.929527

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '54978br', 'Clabel': '54978br1', 'Cnumber': 1, 'abc_quality': 1.0219861987163863, 'absD': 1311981684929612218368, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1848, 'ainvs': [1, 1, 1, -10066953, 12165719607], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 54978, 'degree': 4147200, 'elladic_images': ['8.6.0.4', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8645938148526761036648828633', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 40, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [959024269496848362625, 11151660319506432], 'lmfdb_iso': '54978.bo', 'lmfdb_label': '54978.bo3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -205448, -35497920], 'min_quad_twist_disc': -7, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.d.1', '21.8.0-3.a.1.1', '24.24.0.bx.1', '42.24.0-6.a.1.3', '66.24.0.b.1', '168.48.0.?', '264.48.1.?', '462.48.0.?', '1848.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.62867335727335982891474884882', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8916387403250194511122064916', 'prec': 100}, 'szpiro_ratio': 5.496071609039273, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 1, -1, 1, 0, -1, 0, 1, 1, 0, 1, -1, 4, 0, 0, 1, 1, 1, -8, 0], 'aplist': [1, -1, 0, 0, 1, 4, 1, -8, 6, 6, 4, 2, 6, -4, -6, -12, 0, 4, -4, 6, -2, -10, -12, -18, -14], 'class_deg': 6, 'class_size': 4, 'conductor': 54978, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '54978.bo', 'trace_hash': 1710881121123555904}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.0032497161344367932246336990801', 'prec': 110}, 'conductor': 54978, 'gens': [[1287, 36008, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.62867335727335982891474884882', 'prec': 103}], 'lmfdb_label': '54978.bo3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.15325869262121039570021760533', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.6714691139352014976507690826870119467', 'prec': 130}, 'tamagawa_product': 360, 'torsion_generators': [[1679, -840, 1]], 'xcoord_integral_points': [1287, 1679, 2255, 5775]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [5, 0], '5': [1, 1, 0], '7': 'a', '11': [2, 0], '13': [1, 0], '17': [2, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '54978.bo3'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 2656636
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '54978.bo3', 'torsion': [2, 2]}
  • id: 2656637
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '54978.bo3', 'torsion': [6]}
  • id: 2656639
    {'degree': 4, 'field': [100, 0, -13, 0, 1], 'lmfdb_label': '54978.bo3', 'torsion': [2, 6]}
  • id: 2656638
    {'degree': 4, 'field': [102, -4, 5, -2, 1], 'lmfdb_label': '54978.bo3', 'torsion': [4]}
  • id: 2656640
    {'degree': 6, 'field': [-12, -6, -29, -33, 2, -3, 1], 'lmfdb_label': '54978.bo3', 'torsion': [6]}
  • id: 2656643
    {'degree': 8, 'field': [36, 0, -20, 0, 21, 0, 6, 0, 1], 'lmfdb_label': '54978.bo3', 'torsion': [12]}
  • id: 2656641
    {'degree': 8, 'field': [2304, -2688, 1648, -320, -82, 52, 5, -2, 1], 'lmfdb_label': '54978.bo3', 'torsion': [2, 4]}
  • id: 2656642
    {'degree': 8, 'field': [15526984, 3241832, -1403116, -37840, 27322, 82, -301, -2, 1], 'lmfdb_label': '54978.bo3', 'torsion': [2, 4]}
  • id: 2656644
    {'degree': 12, 'field': [16, -216, 968, 54, 363, 9, 205, -138, -6, 12, -1, -3, 1], 'lmfdb_label': '54978.bo3', 'torsion': [3, 6]}
  • id: 2656645
    {'degree': 12, 'field': [144, 0, 1188, 0, 1069, 0, -8325, 0, -868, 0, -9, 0, 1], 'lmfdb_label': '54978.bo3', 'torsion': [2, 6]}
  • id: 2656647
    {'degree': 16, 'field': [2304, -8064, 12144, -16560, 25132, -25336, 17724, -10600, 6825, -2012, 1224, -596, 138, -28, 12, -4, 1], 'lmfdb_label': '54978.bo3', 'torsion': [2, 12]}
  • id: 2656646
    {'degree': 16, 'field': [981802368, 295332864, 987351296, 78254720, 273614128, 9887808, 37586192, 338880, 3281996, -18896, 180600, -1312, 6156, -24, 120, 0, 1], 'lmfdb_label': '54978.bo3', 'torsion': [8]}
  • id: 2656648
    {'degree': 16, 'field': [144413887552, -141775993568, 65165333640, -14937454840, 406168524, 790205592, -223689914, 20843402, 4232973, -1535198, 164980, 6090, -4626, 574, 6, -4, 1], 'lmfdb_label': '54978.bo3', 'torsion': [2, 12]}
  • id: 2656649
    {'degree': 18, 'field': [1092634138208, 56658850080, 47376446304, -12792727072, 35309061552, 10313133120, 4562349566, -113956554, 235367946, -84464057, 13404645, -4318302, 678640, -90468, 18132, -856, 222, -3, 1], 'lmfdb_label': '54978.bo3', 'torsion': [18]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 1320768
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 30, 'j_denominator_valuation': 30, 'kodaira_symbol': 34, 'lmfdb_label': '54978.bo3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 30}
  • id: 1320769
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '54978.bo3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1320770
    {'conductor': 54978, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '54978.bo3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1320771
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '54978.bo3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1320772
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '54978.bo3', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2029406
    {'adelic_gens': [[1450, 1323, 1365, 1576], [50, 539, 693, 1828], [925, 1596, 798, 337], [15, 322, 1022, 533], [1, 0, 12, 1], [11, 2, 1798, 1839], [1837, 12, 1836, 13], [1, 6, 6, 37], [1, 12, 0, 1], [263, 0, 0, 1847]], 'adelic_image': '1848.96.1.?', 'conductor': 54978, 'lmfdb_label': '54978.bo3', 'prime': 0}
  • id: 234362
    {'conductor': 54978, 'elladic_image': '8.6.0.4', 'lmfdb_label': '54978.bo3', 'modell_image': '2B', 'prime': 2}
  • id: 234363
    {'conductor': 54978, 'elladic_image': '3.4.0.1', 'lmfdb_label': '54978.bo3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 2781518
    {'lmfdb_iso': '54978.bo', 'p': 13, 'prec': 20, 'unit': 1335661381737311875374, 'val': 1}
  • id: 2781520
    {'lmfdb_iso': '54978.bo', 'p': 19, 'prec': 20, 'unit': 197083596668153806632793, 'val': 1}
  • id: 2781523
    {'lmfdb_iso': '54978.bo', 'p': 23, 'prec': 20, 'unit': 18916320811443217349472125, 'val': 1}
  • id: 2781517
    {'lmfdb_iso': '54978.bo', 'p': 29, 'prec': 20, 'unit': 5102695811339580641890493731, 'val': 1}
  • id: 2781527
    {'lmfdb_iso': '54978.bo', 'p': 31, 'prec': 20, 'unit': 6651089207553099066551310501, 'val': 1}
  • id: 2781513
    {'lmfdb_iso': '54978.bo', 'p': 37, 'prec': 20, 'unit': 551144694920408521931529150793, 'val': 1}
  • id: 2781515
    {'lmfdb_iso': '54978.bo', 'p': 41, 'prec': 20, 'unit': 3484255255869179794081840439454, 'val': 1}
  • id: 2781516
    {'lmfdb_iso': '54978.bo', 'p': 43, 'prec': 20, 'unit': 9909839224461111129411802425871, 'val': 1}
  • id: 2781519
    {'lmfdb_iso': '54978.bo', 'p': 47, 'prec': 20, 'unit': 56737289245613455973002170697820, 'val': 1}
  • id: 2781521
    {'lmfdb_iso': '54978.bo', 'p': 53, 'prec': 20, 'unit': 76857409553072795592892364852891, 'val': 1}
  • id: 2781526
    {'lmfdb_iso': '54978.bo', 'p': 61, 'prec': 20, 'unit': 3637402907846054261318344877971614, 'val': 1}
  • id: 2781512
    {'lmfdb_iso': '54978.bo', 'p': 67, 'prec': 20, 'unit': 10533307530911683370299457502907134, 'val': 1}
  • id: 2781514
    {'lmfdb_iso': '54978.bo', 'p': 71, 'prec': 20, 'unit': 63558663415326084461479029625612788, 'val': 1}
  • id: 2781522
    {'lmfdb_iso': '54978.bo', 'p': 73, 'prec': 20, 'unit': 165403966985555091111763694730783040, 'val': 1}
  • id: 2781525
    {'lmfdb_iso': '54978.bo', 'p': 79, 'prec': 20, 'unit': 9998979425722281144534773683829407, 'val': 1}
  • id: 2781511
    {'lmfdb_iso': '54978.bo', 'p': 83, 'prec': 20, 'unit': 1448622429739288266572678022039159615, 'val': 1}
  • id: 2781524
    {'lmfdb_iso': '54978.bo', 'p': 89, 'prec': 20, 'unit': 6141526074853219334051105843556512634, 'val': 1}
  • id: 2781510
    {'lmfdb_iso': '54978.bo', 'p': 97, 'prec': 20, 'unit': 3684082676846010399091715156163692240, 'val': 1}